{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multisensor Data Fusion with acceleration ($\\ddot x$ and $\\ddot y$) and position ($x$ and $y$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm\n",
    "from sympy import Symbol, Matrix\n",
    "from sympy.interactive import printing\n",
    "printing.init_printing()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## State Vector\n",
    "Constant Acceleration Model for Ego Motion in Plane\n",
    "$$x_k= \\left[ \\begin{matrix} x \\\\ y \\\\ \\dot x \\\\ \\dot y \\\\ \\ddot x \\\\ \\ddot y \\end{matrix} \\right]$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.]\n",
      " [ 0.]\n",
      " [ 0.]\n",
      " [ 0.]\n",
      " [ 0.]\n",
      " [ 0.]] (6, 1)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1fd44eb0400>"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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An6wq/8CXpAU26KOkHcCN3faNwKf6zHkIWJ9kXZIVwHXdOpJcBbwd+JmqemHAWiRJQzBo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\nJDX+Bbr8mccwhaWSAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fd44344208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.matrix([[0.0, 0.0, 0.0, 0.0, 0.0, 0.0]]).T\n",
    "print(x, x.shape)\n",
    "n=x.size # States\n",
    "plt.scatter(float(x[0]),float(x[1]), s=100)\n",
    "plt.title('Initial Location')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 100.    0.    0.    0.    0.    0.]\n",
      " [   0.  100.    0.    0.    0.    0.]\n",
      " [   0.    0.   10.    0.    0.    0.]\n",
      " [   0.    0.    0.   10.    0.    0.]\n",
      " [   0.    0.    0.    0.    1.    0.]\n",
      " [   0.    0.    0.    0.    0.    1.]] (6, 6)\n"
     ]
    }
   ],
   "source": [
    "P = np.diag([100.0, 100.0, 10.0, 10.0, 1.0, 1.0])\n",
    "print(P, P.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Time Step between Filter Steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.     0.     0.1    0.     0.005  0.   ]\n",
      " [ 0.     1.     0.     0.1    0.     0.005]\n",
      " [ 0.     0.     1.     0.     0.1    0.   ]\n",
      " [ 0.     0.     0.     1.     0.     0.1  ]\n",
      " [ 0.     0.     0.     0.     1.     0.   ]\n",
      " [ 0.     0.     0.     0.     0.     1.   ]] (6, 6)\n"
     ]
    }
   ],
   "source": [
    "dt = 0.1 \n",
    "\n",
    "A = np.matrix([[1.0, 0.0, dt, 0.0, 1/2.0*dt**2, 0.0],\n",
    "              [0.0, 1.0, 0.0, dt, 0.0, 1/2.0*dt**2],\n",
    "              [0.0, 0.0, 1.0, 0.0, dt, 0.0],\n",
    "              [0.0, 0.0, 0.0, 1.0, 0.0, dt],\n",
    "              [0.0, 0.0, 0.0, 0.0, 1.0, 0.0],\n",
    "              [0.0, 0.0, 0.0, 0.0, 0.0, 1.0]])\n",
    "print(A, A.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  0.  0.  0.  0.  0.]\n",
      " [ 0.  1.  0.  0.  0.  0.]\n",
      " [ 0.  0.  0.  0.  1.  0.]\n",
      " [ 0.  0.  0.  0.  0.  1.]] (4, 6)\n"
     ]
    }
   ],
   "source": [
    "H = np.matrix([[1.0, 0.0, 0.0, 0.0, 0.0, 0.0],\n",
    "               [0.0, 1.0, 0.0, 0.0, 0.0, 0.0],\n",
    "               [0.0, 0.0, 0.0, 0.0, 1.0, 0.0],\n",
    "              [0.0, 0.0, 0.0, 0.0, 0.0, 1.0]])\n",
    "print(H, H.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\left[\\begin{matrix}0.25 \\Delta t^{4} & 0.25 \\Delta t^{4} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2}\\\\0.25 \\Delta t^{4} & 0.25 \\Delta t^{4} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & 0.5 \\Delta t^{2} & 0.5 \\Delta t^{2}\\\\0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & \\Delta t^{2} & \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t\\\\0.5 \\Delta t^{3} & 0.5 \\Delta t^{3} & \\Delta t^{2} & \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t\\\\0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 & 1.0\\\\0.5 \\Delta t^{2} & 0.5 \\Delta t^{2} & 1.0 \\Delta t & 1.0 \\Delta t & 1.0 & 1.0\\end{matrix}\\right]$$"
      ],
      "text/plain": [
       "⎡             4               4              3              3              2  \n",
       "⎢0.25⋅\\Delta t   0.25⋅\\Delta t   0.5⋅\\Delta t   0.5⋅\\Delta t   0.5⋅\\Delta t   \n",
       "⎢                                                                             \n",
       "⎢             4               4              3              3              2  \n",
       "⎢0.25⋅\\Delta t   0.25⋅\\Delta t   0.5⋅\\Delta t   0.5⋅\\Delta t   0.5⋅\\Delta t   \n",
       "⎢                                                                             \n",
       "⎢            3               3             2              2                   \n",
       "⎢0.5⋅\\Delta t    0.5⋅\\Delta t      \\Delta t       \\Delta t     1.0⋅\\Delta t   \n",
       "⎢                                                                             \n",
       "⎢            3               3             2              2                   \n",
       "⎢0.5⋅\\Delta t    0.5⋅\\Delta t      \\Delta t       \\Delta t     1.0⋅\\Delta t   \n",
       "⎢                                                                             \n",
       "⎢            2               2                                                \n",
       "⎢0.5⋅\\Delta t    0.5⋅\\Delta t    1.0⋅\\Delta t   1.0⋅\\Delta t        1.0       \n",
       "⎢                                                                             \n",
       "⎢            2               2                                                \n",
       "⎣0.5⋅\\Delta t    0.5⋅\\Delta t    1.0⋅\\Delta t   1.0⋅\\Delta t        1.0       \n",
       "\n",
       "            2⎤\n",
       "0.5⋅\\Delta t ⎥\n",
       "             ⎥\n",
       "            2⎥\n",
       "0.5⋅\\Delta t ⎥\n",
       "             ⎥\n",
       "             ⎥\n",
       "1.0⋅\\Delta t ⎥\n",
       "             ⎥\n",
       "             ⎥\n",
       "1.0⋅\\Delta t ⎥\n",
       "             ⎥\n",
       "             ⎥\n",
       "     1.0     ⎥\n",
       "             ⎥\n",
       "             ⎥\n",
       "     1.0     ⎦"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dts = Symbol('\\Delta t')\n",
    "Qs = Matrix([[0.5*dts**2],[0.5*dts**2],[dts],[dts],[1.0],[1.0]])\n",
    "Qs*Qs.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  2.50000000e-11   2.50000000e-11   5.00000000e-10   5.00000000e-10\n",
      "    5.00000000e-09   5.00000000e-09]\n",
      " [  2.50000000e-11   2.50000000e-11   5.00000000e-10   5.00000000e-10\n",
      "    5.00000000e-09   5.00000000e-09]\n",
      " [  5.00000000e-10   5.00000000e-10   1.00000000e-08   1.00000000e-08\n",
      "    1.00000000e-07   1.00000000e-07]\n",
      " [  5.00000000e-10   5.00000000e-10   1.00000000e-08   1.00000000e-08\n",
      "    1.00000000e-07   1.00000000e-07]\n",
      " [  5.00000000e-09   5.00000000e-09   1.00000000e-07   1.00000000e-07\n",
      "    1.00000000e-06   1.00000000e-06]\n",
      " [  5.00000000e-09   5.00000000e-09   1.00000000e-07   1.00000000e-07\n",
      "    1.00000000e-06   1.00000000e-06]] (6, 6)\n"
     ]
    }
   ],
   "source": [
    "sa = 0.001\n",
    "G = np.matrix([[1/2.0*dt**2],\n",
    "               [1/2.0*dt**2],\n",
    "               [dt],\n",
    "               [dt],\n",
    "               [1.0],\n",
    "               [1.0]])\n",
    "Q = G*G.T*sa**2\n",
    "\n",
    "print(Q, Q.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.  0.  0.  0.  0.  0.]\n",
      " [ 0.  1.  0.  0.  0.  0.]\n",
      " [ 0.  0.  1.  0.  0.  0.]\n",
      " [ 0.  0.  0.  1.  0.  0.]\n",
      " [ 0.  0.  0.  0.  1.  0.]\n",
      " [ 0.  0.  0.  0.  0.  1.]] (6, 6)\n"
     ]
    }
   ],
   "source": [
    "I = np.eye(n)\n",
    "print(I, I.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Measurements\n",
    "#### Assumption of  update rates:\n",
    "\n",
    "1.Acceleration from IMU with 10Hz\n",
    "\n",
    "2.Position from GPS with 1Hz\n",
    "\n",
    "Which means, that every 10th of an acceleration measurement, there is a new position measurement from GPS. The Kalman Filter can perfectly handle this unsynchronous measurement incoming.\n",
    "\n",
    "\n",
    "## Intialize:\n",
    "\n",
    "*\n",
    "1. Measurements\n",
    "2.  Sigma for position\n",
    "3.  x Position\n",
    "4.  y Position\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Measurement Noise Covariance $R$\n",
    "\n",
    "#### Intialize:\n",
    "1.  ##### Noise of Acceleration Measurement $ra$\n",
    "2.  ##### Noise of Position Measurement $rp$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 10000.      0.      0.      0.]\n",
      " [     0.  10000.      0.      0.]\n",
      " [     0.      0.    100.      0.]\n",
      " [     0.      0.      0.    100.]] (4, 4)\n"
     ]
    }
   ],
   "source": [
    "ra = 10.0**2   # Noise of Acceleration Measurement\n",
    "rp = 100.0**2  # Noise of Position Measurement\n",
    "R = np.matrix([[rp, 0.0, 0.0, 0.0],\n",
    "               [0.0, rp, 0.0, 0.0],\n",
    "               [0.0, 0.0, ra, 0.0],\n",
    "               [0.0, 0.0, 0.0, ra]])\n",
    "print(R, R.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m = 700\n",
    "\n",
    "sp= 1.0 \n",
    "px= 0.0\n",
    "py= 0.0 \n",
    "\n",
    "mpx = np.array(px+sp*np.random.randn(m))\n",
    "mpy = np.array(py+sp*np.random.randn(m))\n",
    "\n",
    "# Generate GPS Trigger\n",
    "GPS=np.ndarray(m,dtype='bool')\n",
    "GPS[0]=True\n",
    "# Less new position updates\n",
    "for i in range(1,m):\n",
    "    if i%10==0:\n",
    "        GPS[i]=True\n",
    "    else:\n",
    "        mpx[i]=mpx[i-1]\n",
    "        mpy[i]=mpy[i-1]\n",
    "        GPS[i]=False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ True, False, False, False, False, False, False, False, False,\n",
       "       False,  True, False, False, False, False, False, False, False,\n",
       "       False, False,  True, False, False, False, False, False, False,\n",
       "       False, False, False,  True, False, False, False, False, False,\n",
       "       False, False, False, False,  True, False, False, False, False,\n",
       "       False, False, False, False, False,  True, False, False, False,\n",
       "       False, False, False, False, False, False,  True, False, False,\n",
       "       False, False, False, False, False, False, False,  True, False,\n",
       "       False, False, False, False, False, False, False, False,  True,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "        True, False, False, False, False, False, False, False, False,\n",
       "       False,  True, False, False, False, False, False, False, False,\n",
       "       False, False,  True, False, False, False, False, False, False,\n",
       "       False, False, False,  True, False, False, False, False, False,\n",
       "       False, False, False, False,  True, False, False, False, False,\n",
       "       False, False, False, False, False,  True, False, False, False,\n",
       "       False, False, False, False, False, False,  True, False, False,\n",
       "       False, False, False, False, False, False, False,  True, False,\n",
       "       False, False, False, False, False, False, False, False,  True,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "        True, False, False, False, False, False, False, False, False,\n",
       "       False,  True, False, False, False, False, False, False, False,\n",
       "       False, False,  True, False, False, False, False, False, False,\n",
       "       False, False, False,  True, False, False, False, False, False,\n",
       "       False, False, False, False,  True, False, False, False, False,\n",
       "       False, False, False, False, False,  True, False, False, False,\n",
       "       False, False, False, False, False, False,  True, False, False,\n",
       "       False, False, False, False, False, False, False,  True, False,\n",
       "       False, False, False, False, False, False, False, False,  True,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "        True, False, False, False, False, False, False, False, False,\n",
       "       False,  True, False, False, False, False, False, False, False,\n",
       "       False, False,  True, False, False, False, False, False, False,\n",
       "       False, False, False,  True, False, False, False, False, False,\n",
       "       False, False, False, False,  True, False, False, False, False,\n",
       "       False, False, False, False, False,  True, False, False, False,\n",
       "       False, False, False, False, False, False,  True, False, False,\n",
       "       False, False, False, False, False, False, False,  True, False,\n",
       "       False, False, False, False, False, False, False, False,  True,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "        True, False, False, False, False, False, False, False, False,\n",
       "       False,  True, False, False, False, False, False, False, False,\n",
       "       False, False,  True, False, False, False, False, False, False,\n",
       "       False, False, False,  True, False, False, False, False, False,\n",
       "       False, False, False, False,  True, False, False, False, False,\n",
       "       False, False, False, False, False,  True, False, False, False,\n",
       "       False, False, False, False, False, False,  True, False, False,\n",
       "       False, False, False, False, False, False, False,  True, False,\n",
       "       False, False, False, False, False, False, False, False,  True,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "        True, False, False, False, False, False, False, False, False,\n",
       "       False,  True, False, False, False, False, False, False, False,\n",
       "       False, False,  True, False, False, False, False, False, False,\n",
       "       False, False, False,  True, False, False, False, False, False,\n",
       "       False, False, False, False,  True, False, False, False, False,\n",
       "       False, False, False, False, False,  True, False, False, False,\n",
       "       False, False, False, False, False, False,  True, False, False,\n",
       "       False, False, False, False, False, False, False,  True, False,\n",
       "       False, False, False, False, False, False, False, False,  True,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "        True, False, False, False, False, False, False, False, False,\n",
       "       False,  True, False, False, False, False, False, False, False,\n",
       "       False, False,  True, False, False, False, False, False, False,\n",
       "       False, False, False,  True, False, False, False, False, False,\n",
       "       False, False, False, False,  True, False, False, False, False,\n",
       "       False, False, False, False, False,  True, False, False, False,\n",
       "       False, False, False, False, False, False,  True, False, False,\n",
       "       False, False, False, False, False, False, False,  True, False,\n",
       "       False, False, False, False, False, False, False, False,  True,\n",
       "       False, False, False, False, False, False, False, False, False,\n",
       "        True, False, False, False, False, False, False, False, False,\n",
       "       False,  True, False, False, False, False, False, False, False,\n",
       "       False, False,  True, False, False, False, False, False, False,\n",
       "       False, False, False,  True, False, False, False, False, False,\n",
       "       False, False, False, False,  True, False, False, False, False,\n",
       "       False, False, False, False, False,  True, False, False, False,\n",
       "       False, False, False, False, False, False,  True, False, False,\n",
       "       False, False, False, False, False, False, False], dtype=bool)"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GPS"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Acceleration\n",
    "### Sigma for acceleration in X and Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [],
   "source": [
    "sa= 0.1 \n",
    "ax= 0.0 \n",
    "ay= 0.0 \n",
    "\n",
    "mx = np.array(ax+sa*np.random.randn(m))\n",
    "my = np.array(ay+sa*np.random.randn(m))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(4, 700)\n"
     ]
    }
   ],
   "source": [
    "measurements = np.vstack((mpx,mpy,mx,my))\n",
    "print(measurements.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.6889478 , -0.6889478 , -0.6889478 , ..., -0.64087444,\n",
       "        -0.64087444, -0.64087444],\n",
       "       [ 2.05407023,  2.05407023,  2.05407023, ..., -0.3029827 ,\n",
       "        -0.3029827 , -0.3029827 ],\n",
       "       [ 0.11503533,  0.09070637,  0.00233711, ..., -0.00781765,\n",
       "         0.15003673, -0.1805174 ],\n",
       "       [-0.10450718,  0.07364729,  0.02905628, ..., -0.02025587,\n",
       "        -0.14383184, -0.06314529]])"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_measurements():\n",
    "    fig = plt.figure(figsize=(16,9))\n",
    "    plt.subplot(211)\n",
    "    plt.step(range(m),mpx, label='$x$')\n",
    "    plt.step(range(m),mpy, label='$y$')\n",
    "    plt.ylabel(r'Position $m$')\n",
    "    plt.title('Measurements')\n",
    "    plt.ylim([-10, 10])\n",
    "    plt.legend(loc='best',prop={'size':18})\n",
    "\n",
    "    plt.subplot(212)\n",
    "    plt.step(range(m),mx, label='$a_x$')\n",
    "    plt.step(range(m),my, label='$a_y$')\n",
    "    plt.ylabel(r'Acceleration $m/s^2$')\n",
    "    plt.ylim([-1, 1])\n",
    "    plt.legend(loc='best',prop={'size':18})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EJMWiE+9IPBL9b6biWEREREREJIUikQj19fWpTiPj1NfXE4lEErY/FcciIiIiIiIpVFxc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\nJLW8/w8laVcdRF2f2wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fd445373c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_measurements()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Preallocation for Plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xt = []\n",
    "yt = []\n",
    "dxt= []\n",
    "dyt= []\n",
    "ddxt=[]\n",
    "ddyt=[]\n",
    "Zx = []\n",
    "Zy = []\n",
    "Px = []\n",
    "Py = []\n",
    "Pdx= []\n",
    "Pdy= []\n",
    "Pddx=[]\n",
    "Pddy=[]\n",
    "Kx = []\n",
    "Ky = []\n",
    "Kdx= []\n",
    "Kdy= []\n",
    "Kddx=[]\n",
    "Kddy=[]\n",
    "\n",
    "\n",
    "def savestates(x, Z, P, K):\n",
    "    xt.append(float(x[0]))\n",
    "    yt.append(float(x[1]))\n",
    "    dxt.append(float(x[2]))\n",
    "    dyt.append(float(x[3]))\n",
    "    ddxt.append(float(x[4]))\n",
    "    ddyt.append(float(x[5]))\n",
    "    Zx.append(float(Z[0]))\n",
    "    Zy.append(float(Z[1]))\n",
    "    Px.append(float(P[0,0]))\n",
    "    Py.append(float(P[1,1]))\n",
    "    Pdx.append(float(P[2,2]))\n",
    "    Pdy.append(float(P[3,3]))\n",
    "    Pddx.append(float(P[4,4]))\n",
    "    Pddy.append(float(P[5,5]))\n",
    "    Kx.append(float(K[0,0]))\n",
    "    Ky.append(float(K[1,0]))\n",
    "    Kdx.append(float(K[2,0]))\n",
    "    Kdy.append(float(K[3,0]))\n",
    "    Kddx.append(float(K[4,0]))\n",
    "    Kddy.append(float(K[5,0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The Usual Step :\n",
    "1.  ##### Time Update (Prediction)\n",
    "2.  ##### Project the state ahead\n",
    "3.  ##### Project the error covariance ahead\n",
    "4.  ##### Measurement Update (Correction)\n",
    "5.  ##### if there is a GPS Measurement: Compute the Kalman Gain\n",
    "6.  ##### Update the estimate via z\n",
    "7.  ##### Update the error covariance\n",
    "8.  ##### Save states for Plotting\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 160,
   "metadata": {},
   "outputs": [],
   "source": [
    "for kalman_filter in range(m):   \n",
    "    x = A*x    \n",
    "    P = A*P*A.T + Q  \n",
    "    \n",
    "    if GPS[kalman_filter]:        \n",
    "        S = H*P*H.T + R\n",
    "        K = (P*H.T) * np.linalg.pinv(S)        \n",
    "        Z = measurements[:,kalman_filter].reshape(H.shape[0],1)\n",
    "        y = Z - (H*x)                            # Innovation or Residual\n",
    "        x = x + (K*y)              \n",
    "        P = (I - (K*H))*P\n",
    "\n",
    "   \n",
    "    \n",
    "    \n",
    "    savestates(x, Z, P, K)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_P():\n",
    "    fig = plt.figure(figsize=(16,9))\n",
    "    plt.subplot(211)\n",
    "    plt.plot(range(len(measurements[0])),Px, label='$x$')\n",
    "    plt.plot(range(len(measurements[0])),Py, label='$y$')\n",
    "    plt.title('Uncertainty (Elements from Matrix $P$)')\n",
    "    plt.legend(loc='best',prop={'size':22})\n",
    "    plt.subplot(212)\n",
    "    plt.plot(range(len(measurements[0])),Pddx, label='$\\ddot x$')\n",
    "    plt.plot(range(len(measurements[0])),Pddy, label='$\\ddot y$')\n",
    "\n",
    "    plt.xlabel('Filter Step')\n",
    "    plt.ylabel('')\n",
    "    plt.legend(loc='best',prop={'size':22})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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H2kcCxQpYWrx/5QsAbPGNyVurlFJKKaWUOvdpkO0mlhNke03Kv8NxImwOOrQU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\naZT/Dy9YHpMbGPC3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fd449efe10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_P()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_K_ddxy():\n",
    "    fig = plt.figure(figsize=(16,9))\n",
    "    #plt.plot(range(len(measurements[0])),Kx, label='Kalman Gain for $x$')\n",
    "    #plt.plot(range(len(measurements[0])),Ky, label='Kalman Gain for $y$')\n",
    "    #plt.plot(range(len(measurements[0])),Kdx, label='Kalman Gain for $\\dot x$')\n",
    "    #plt.plot(range(len(measurements[0])),Kdy, label='Kalman Gain for $\\dot y$')\n",
    "    plt.plot(range(len(measurements[0])),Kddx, label='Kalman Gain for $\\ddot x$')\n",
    "    plt.plot(range(len(measurements[0])),Kddy, label='Kalman Gain for $\\ddot y$')\n",
    "\n",
    "    plt.xlabel('Filter Step')\n",
    "    plt.ylabel('')\n",
    "    plt.title('Kalman Gain (the lower, the more the measurement fullfill the prediction)')\n",
    "    plt.legend(loc='best',prop={'size':18})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4X7dJmuS/NleHuM3F8r7/t8hbmCnUgBUur8u79dIGM9scrHETz/dseYvMbZC3SGG9K46H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\nAAAAAIDYI/wCAAAAAGLv/wNvmXWPRvzrdgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fd449249e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_K_ddxy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_K_dxy():\n",
    "    fig = plt.figure(figsize=(16,9))\n",
    "    #plt.plot(range(len(measurements[0])),Kx, label='Kalman Gain for $x$')\n",
    "    #plt.plot(range(len(measurements[0])),Ky, label='Kalman Gain for $y$')\n",
    "    plt.plot(range(len(measurements[0])),Kdx, label='Kalman Gain for $\\dot x$')\n",
    "    plt.plot(range(len(measurements[0])),Kdy, label='Kalman Gain for $\\dot y$')\n",
    "    #plt.plot(range(len(measurements[0])),Kddx, label='Kalman Gain for $\\ddot x$')\n",
    "    #plt.plot(range(len(measurements[0])),Kddy, label='Kalman Gain for $\\ddot y$')\n",
    "\n",
    "    plt.xlabel('Filter Step for dx and dy')\n",
    "    plt.ylabel('')\n",
    "    plt.title('Kalman Gain (the lower, the more the measurement fullfill the prediction)')\n",
    "    plt.legend(loc='best',prop={'size':18})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AAAAQLB988IHOPPNMTZ8+XcOHD49IDpFc7OlmSWOcc7mSxkh6pqYgM7vRN4d2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\nAACAVCHIAgAAAABShSALAAAAAEiV/wGCMALbZp0/MwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fd44182be0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_K_dxy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_K_xy():\n",
    "    fig = plt.figure(figsize=(16,9))\n",
    "    plt.plot(range(len(measurements[0])),Kx, label='Kalman Gain for $x$')\n",
    "    plt.plot(range(len(measurements[0])),Ky, label='Kalman Gain for $y$')\n",
    "    #plt.plot(range(len(measurements[0])),Kdx, label='Kalman Gain for $\\dot x$')\n",
    "    #plt.plot(range(len(measurements[0])),Kdy, label='Kalman Gain for $\\dot y$')\n",
    "    #plt.plot(range(len(measurements[0])),Kddx, label='Kalman Gain for $\\ddot x$')\n",
    "    #plt.plot(range(len(measurements[0])),Kddy, label='Kalman Gain for $\\ddot y$')\n",
    "\n",
    "    plt.xlabel('Filter Step for x and y')\n",
    "    plt.ylabel('')\n",
    "    plt.title('Kalman Gain (the lower, the more the measurement fullfill the prediction)')\n",
    "    plt.legend(loc='best',prop={'size':18})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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kpAS/K0hNpoJVjtKlZX0AvsnYqYJVREREpBr48MMPueKKK0hISGD69Om1vshZ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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1fd44924a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_K_xy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
